Apparatus and method for investigating semiconductors wafer

ABSTRACT

In order to determine the dielectric constant of a layer deposited on a semiconducotr wafer ( 2 ), the density of the layer is obtained. To obtain that density, the wafer ( 2 ) without the layer is weighed in a weighing chamber ( 4 ) in which a weighing pan ( 7 ) supports the wafer on a weighing balance. The weight of the wafer is determined taking into account the buoyancy exerted by the air on the wafer ( 2 ). Then the layer is deposited on the wafer ( 2 ) and the weighing operation repeated. Alternatively a reference wafer may be used. If the material of the layer is known, the weight of the layer can be used to derive its density using a thickness measurement. Alternatively, if the density is known, the thickness can be obtained.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to the investigation ofsemiconductor wafers. It relates particularly, but not exclusively, tothe determination of the mass, weight and/or dielectric constant of alayer deposited on such a wafer.

[0003] It also relates to the investigation of thickness of layersdeposited on such a wafer.

[0004] 2. Summary of the Prior Art

[0005] It is already known to investigate the thickness of a layer on asemiconductor waver, but existing thickness methods are specific to thetype of material applied to the wafer. For example, when the layer is aninsulator deposited the layer, its thickness investigated byellipsometry or spectral reflectivity, whereas if the layer deposited isa metal, its thickness is investigated by measuring its surfaceresistivity. When a layer is subsequently etched, its subsequentthickness may be measured by interferometry or by using a serviceprofiler.

SUMMARY OF THE INVENTION

[0006] The present invention has its origin in the realisation that thedetermination of the mass or weight of a layer deposited on asemiconductor wafer may enable various properties of the wafersubsequently to be determined. In particular:

[0007] (1) If the mass of the layer can be determined, then thethickness of the layer can be determined if the density of the materialis known;

[0008] (2) If both the mass and the thickness of the layer can bedetermined, then its density can be determined;

[0009] (3) If the density of a layer can be determined, then it has beenrealised that there is a relationship between the density and thedielectric constant of the layer, and hence it is possible to determinethe dielectric constant from the density.

[0010] (4) In Statistical Process Control of semiconductor wafers,measurements of the thickness of the layer have been used as a guide tothe consistency of the processes being used. However, as mentionedabove, known ways of measuring thickness are dependent on the material.It has been realised that mass or weight of the layer itself gives aguide to the consistency of the process.

[0011] The present invention has several aspects, concerned withapplying these realisations.

[0012] In the first aspect, the mass or weight of the layer and thethickness of the layer are measured, to obtain a value representing thedensity of the layer. From that density measurement, the dielectricconstant is determined.

[0013] The thickness of the layer may be obtained by one or more of theknown methods referred to above. To determine the weight or mass,several methods may be used. For example, the weight of thesemiconductor wafer both before and after the layer is formed thereonmay be compared with a calibration weight having the same density as thesemiconductor wafer. Alternatively, the weight of the wafer with thelayer to be measured may be compared with a reference semiconductorwafer. As another alternative, the layer may be weighed under vacuumusing an appropriate balance.

[0014] However, such weighing methods are prone to inaccuracies. It hasbeen realised that if the wafer is weighed in air, and a correction ismade for the buoyancy exerted on the wafer by the air an accuratemeasurement of the mass of the layer deposited on the layer may bedetermined. Although the use of such a buoyancy correction may be usedin the first aspect of the invention, the use of a buoyancy correctionto determine the mass or weight of a layer on a semiconductor waferrepresents a second independent aspect of the invention.

[0015] In this second aspect, the present invention relates to aweighing apparatus and a method of weighing thin layers on the surfaceof semiconductor wafers which compensates for such variations in ambientconditions, and in particular to an apparatus or method whichincorporates the buoyancy exerted upon the semiconductor wafer beingweighed into the calculation of the mass of a thin layer deposited onthat wafer.

[0016] The second aspect may then be used in a method of determining thethickness of a thin layer on a semiconductor wafer by determining themass of the layer and calculating the thickness using a known densityvalue, or a method for determining the density of a material depositedon a wafer using a layer of known thickness. Furthermore, the density sodetermined can be used to calculate the dielectric constant of thematerial of the layer.

[0017] Accordingly, the second aspect of the present invention mayprovide an apparatus for weighing a thin-layer deposited on the surfaceof a semi-conductor wafer, the apparatus comprising:

[0018] a weighing chamber containing a weighing instrument to weigh asemiconductor wafer, the weighing instrument having means to receive awafer;

[0019] a temperature sensor, a pressure sensor and a humidity sensor,for monitoring conditions in the weighing chamber; and

[0020] a processor to receive measurements from the temperature,pressure and humidity sensors, the processor being arranged to calculatethe air-density within the chamber from these measurements.

[0021] It is preferred that the weighing instrument has an internalcalibration weight which is used to set the zero and linearity of thereadings for the subsequent measurements. The calibration weight ispreferably made of stainless steel having a density of 8.000 g/cc.

[0022] The buoyancy exerted on the wafer may be calculated from thecalculated air density, the weight of the wafer, the density of thewafer and the density of a calibration wafer used to calibrate thebalance. A suitable formula for calculating the buoyancy exerted on thewafer is described below.

[0023] It is preferred that the processor is arranged to calculate thebuoyancy exerted on the wafer, in which case the processor may receive aweight measurement from the balance and density measurements which maybe input by a user.

[0024] The mass of the wafer can then be calculated by adding thebuoyancy value to the weight measurement. It is preferred that theprocessor is also configured to calculate the mass of the wafer from theweight and buoyancy values.

[0025] The weighing chamber may comprise:

[0026] a housing having a opening for entry of a wafer;

[0027] a weighing instrument in the housing to measure the weight of thewafer, the weighing instrument having a balance in connected to aweighing pan for receiving a wafer; and

[0028] temperature, pressure and humidity monitors, to determine thetemperature, pressure and humidity within the housing.

[0029] The weighing chamber may be made and sold separately from therest of the apparatus and so represents a separate (third) independentaspect of the invention.

[0030] The housing preferably comprises a plurality of side walls, e.g.four, and upper and lower walls. It is preferred that one of the wallsis removable, and can be removed for cleaning, most preferred is thatthe upper wall is a removable lid. The opening may be provided betweenthe upper wall and one of the side walls.

[0031] It is preferred that the opening in the housing through which thearm may be moved is the only opening in the housing, the opening ispreferably relatively small, e.g., the minimum size which allowsmovement of the arm through it, so as minimise the effects of theoutside conditions on the interior of the chamber. An optional door maybe positioned over the opening to shield the opening, for example if theenvironment is particularly prone to draughts.

[0032] Where necessary, an optional DC accelerometer may be used toidentify external vibration or floor movements that might upset theweighing balance.

[0033] It is preferred that the chamber has a divider to divide thechamber into upper and lower chambers, the upper chamber housing theweighing pan and the lower chamber housing the balance, the dividerbeing provided with an aperture through which the connection between theweighing pan and the balance may pass. In this situation it is preferredthat the sensors are located in the upper chamber. Preferably, thechamber walls, including the divider, are made of electrically and/orthermally conductive material.

[0034] The distance between the upper wall of the upper chamber and thedivider is preferably small enough to avoid air convection, but greatenough to minimise the force exerted on the wafer due to the wafersurface. It is preferred that the weighing pan is equidistant from theupper wall of the upper chamber and the divider. The gap between thewafer and either the upper wall of the upper chamber or the divider ispreferably in the range of 5-15 mm.

[0035] The chamber may include a heater, and the interior of theweighing chamber is preferably maintained at a substantially constanttemperature, e.g., within +/−0.1° C. If heated, the enclosure ispreferably maintained within 5° C. of the ambient temperature.

[0036] Preferably, the weighing instrument has readability of 0.01 mgover a range of 0-80 g. For larger than 200 mm wafers the range wouldhave to be extended based on the nominal weight of the wafers. Theinstrument preferably has a repeatability of better than 0.03 mg and atemperature sensitivity drift of less than 1 part in 10⁶/° C.

[0037] The pressure sensor preferably has an accuracy of better than0.04% over the range 800-1200 mbar absolute. Temperature sensitivity ispreferably less than 0.02%/° C. Response time is preferably less than200 ms.

[0038] The temperature sensor preferably has an accuracy of better than0.2° C. and a response time of less than 10 seconds. The humidity sensorpreferably has an accuracy of better than 2% and a response time of lessthan 1 minute.

[0039] The weighing chamber may also be associated with a robotic armcontrolled by a computer, the arm having means releasably to carry awafer, and being moveable from outside the chamber to inside thechamber, through the opening in the housing, to place the wafer on theweighing pan.

[0040] The apparatus may further include a thermal transfer plate toreceive a wafer before it is placed on the weighing pan. Preferably thethermal transfer plate is located within the weighing chamber. Thethermal transfer plate is preferably made of an electrically and/orthermally conducting material, so that any static electricity on thewafer is dispersed before measurement, a preferred material beingaluminium.

[0041] The arm may be capable of carrying a wafer from outside thechamber to the thermal transfer plate, placing the wafer on the thermaltransfer plate and then moving the wafer to the weighing pan.

[0042] The apparatus may further include an anti-static ioniser,comprising a balanced quantity of positive and negative ions used todisperse static electricity within the equipment and on the surface ofthe wafer.

[0043] In a further (fourth) aspect the invention provides a method fordetermining the thickness of a thin-layer deposited on a semiconductorwafer, or for determining the density of a thin-layer deposited on asemiconductor wafer, which method involves determining the mass of thethin-layer, incorporating the effect of the buoyancy exerted upon thewafer during the weighing process. The method may comprise the(non-sequential) steps of:

[0044] placing a wafer on a weighing instrument in a chamber;

[0045] measuring the weight of the wafer;

[0046] determining the air density in the chamber;

[0047] determining the buoyancy exerted on the wafer from the airdensity; and

[0048] determining the mass of the wafer taking into account thebuoyancy exerted upon it;

[0049] repeating the above steps with the wafer with a thin-layerdeposited thereupon;

[0050] subtracting the mass of the wafer without the thin-layerdeposited thereupon, from the mass of the wafer with the thin layerdeposited thereupon to calculate the mass of the layer;

[0051] determining the thickness of the layer from the calculated massof the layer and a known density value of the material of the layer, ordetermining the density of the material from the calculated mass and aknown thickness value.

[0052] Where the mass of the deposited layer is of interest per se, forexample in quality control analysis, the above method may be used tocalculate an accurate mass of the layer and the density or thickness ofthe layer need not be determined. Thus the mass can be determined as analternative to the thickness.

[0053] The method may also be used to determine the thickness of a layerwhich has been removed from a wafer, or to determine the amount ofmaterial removed from a layer, such as when vias (holes) or trenches aremade in a layer. In this situation, the wafer is weighed and the massdetermined as described above, once the layer has been removed, then themass of the wafer measured as set out above and the thickness of thelayer which has been removed is determined by subtraction.

[0054] The method may also be used to determine the weight loss orre-absorption of water or other solvents over time, in the situationwhere the films are not stable.

[0055] For insulating materials, the density value may be used in thesecond aspect of the invention to calculate the dielectric constant ofthe layer. Accordingly, determining the dielectric constant of asubstance from the mass of a thin-layer of that substance deposited on asemiconductor wafer represents a further aspect of the invention.

[0056] The method according to the invention is applicable to a diverserange of materials and is suitable for statistical process control. Itprovides a fast and non-destructive method of achieving accurateresults.

[0057] The air density in the chamber may be determined by measuring thetemperature, pressure and humidity in the chamber and calculating theair density from these parameters. The formula used may be:$\rho_{air} = \frac{\begin{matrix}{{0.3485 \times P} - {0.00132 \times}} \\{\left( {{0.0398 \times T^{2}} - {0.1036 \times T} + 9.5366} \right) \times H}\end{matrix}}{\left( {273.14 + T} \right) \times 1000}$

[0058] Where ρ_(air) is the density of the air in g/cm³, P is thepressure in mBar, T is the temperature in ° C. and H is the relativehumidity in %.

[0059] Alternatively the air density may be calculated by using twocalibration weights of known mass and of different known density. Toreduce errors, it is preferable if the two densities are as far apart aspracticable. This method yields two simultaneous equations involving themeasured weight and the air density from which the air density can becalculated. In this situation, the temperature pressure and humiditysensors may be omitted from the apparatus, or as is preferred, thismethod may be used in addition to the equation given above, as an extralevel of calibration.

[0060] The buoyancy exerted on the wafer may be calculated from the airdensity, the known density of the wafer, for example, the density ofsingle crystal silicon is 2.329 g/cm³, the density of a calibrationweight used to calibrate the balance and the weight of the wafer. Thefollowing formula is preferably used:$B = {W_{w} \times \frac{\left( {\frac{\rho_{air}}{\rho_{w}} - \frac{\rho_{air}}{\rho_{c}}} \right)}{1 - \frac{\rho_{air}}{\rho_{w}}}}$

[0061] Where B is the Buoyancy effect in grams, W_(w) is weight of thewafer in grams, ρ_(w) is the density of the wafer in g/cm³ and ρ_(c) isthe density of the calibration weight used to calibrate the weighingbalance in g/cm³.

[0062] The mass of the wafer with or without the layer may be determinedusing the formula:

M _(w) =W _(w) +B

[0063] The dielectric constant (relative permittivity) of the materialmay be determined from the density using the following formula:$~{ɛ = \frac{{2 \cdot \alpha \cdot \rho} - ɛ_{0}}{{\alpha \cdot \rho} - ɛ_{0}}}$

[0064] Where ε is the dielectric constant, ε₀ is the permittivity offree space, ρ is the density of the film and ∝ is a constant for theparticular type of material in question.

[0065] Alternative methods for determining the thickness or density of alayer include weighing the semiconductor wafers under vacuum. Thistechnique might be preferable where the measurements need to beincorporated into vacuum processing equipment. Or the weighing balancemay be calibrated using a calibration weight having the same density asa semiconductor wafer. Because the air buoyancy is proportional tovolume, the calibration process corrects for it automatically, withoutthe need for independent calculation of the air density. This methodsuffers from the fact that the air density cannot be independentlyverified.

[0066] The invention may also provide a program for a computer, theprogram comprising code to perform the steps of the method describedabove. The program may be stored on a recording medium, for example acomputer disc.

[0067] Another (fifth) aspect of the invention concerns StatisticalProcess Control in the manufacture of semiconductors wafers. This makesuse of the fact that the properties of deposited or etched layers on asemiconductor wafer should be consistent, and therefore the statisticalvariation in those properties provides a measure of the accuracy, orotherwise, of the processes being carried out. Conventionally, thicknessmeasurements have been used to provide statistical analysis, but suchthickness measurements are dependent on the type of material of thelayer, as mentioned above. It has been realised that measurement of themass of the layer may itself be used to provide statistical analysis,and therefore this represents another aspect of the invention.

[0068] Preferably, the mass is measured taking buoyancy into account, ashas previously been mentioned with reference to the second to fourthaspects, but this fifth aspect of the invention is not limited to this.

BRIEF DESCRIPTION OF THE DRAWINGS

[0069] An embodiment of the invention will now be described withreference to the accompanying drawings in which:

[0070]FIG. 1 shows a plan view of the equipment with the lid removed toshow the interior;

[0071]FIG. 2 shows a section through line A-A of the equipment shown inFIG. 1;

[0072]FIG. 3 shows a section through the thermal transfer plate;

[0073]FIG. 4 shows a block diagram of the electronics control;

[0074]FIG. 5 shows a typical relationship between the density and thedielectric constant for carbon doped silicate glass films; and

[0075]FIG. 6 is a diagram of a wafer processing factory in which thepresent invention may be used.

DETAILED DESCRIPTION

[0076] Referring first to FIG. 1, a number of semiconductor wafers 2 areheld within a carrier 1 outside the chamber 4. The robotic arm 3 takeseach wafer in turn and moves it inside the chamber 4 through aperture 10in the walls of chamber, which can be seen in FIG. 2. The arm 3 placesone of the wafers 2 on the thermal transfer plate 5 within the weighingchamber 4. The wafer 2 is left for a period of time, e.g., between 10and 60 seconds while it comes into equilibrium with the temperature ofthe equipment. The robotic arm then takes the wafer from the thermaltransfer plate 5 and places it onto the weighing pan 7 of the weightinstrument, e.g. a Sartorius BP2IID, though any suitable accuratebalance could be used.

[0077] The weight readings are continually monitored until the readinghas settled, usually within 15 to 45 seconds. The robotic arm 3 thenremoves the wafer and places it back into the carrier 1.

[0078] The equipment is mounted on a firm, level surface free fromvibration and not prone to movement (for example bowing of the floor aspeople or equipment move past). The enclosure and balance can be madelevel by using adjusting feet located at each corner of the base of theenclosure.

[0079] The wafer carrier 1 is made of static dissipative material andthe thermal transfer plate is made of an electrically conductingmaterial, so that any static electricity on the wafer is dispersedbefore measurement.

[0080] The interior of the weighing chamber 4 is maintained at asubstantially constant temperature, e.g., within +/−0.1 ° C. Where theambient conditions vary by more than this then the enclosure may beelectrically heated with resistance heaters and maintained at atemperature slightly above ambient. If heated, the enclosure should bemaintained within 5° C. of the ambient temperature, to avoid the risk ofconvection currents.

[0081] Turning now to FIG. 2, the weighing chamber 4 is divided into twoseparate compartments by the divider 8. A lid 9 is shown in position ontop of the chamber in this Figure. The lower compartment 16 houses theweighing balance while the upper compartment 14 houses the weighing pan7, and the wafer 2 when this is on the pan.

[0082] All walls of the chamber, the divider and the lid are made ofmaterials having good electrical and thermal conductivity and are ingood thermal and electrical contact with each other. The chamber shouldbe electrically conducting to prevent any electrical static charge frombuilding up in the vicinity of the weighing instrument.

[0083] The semiconductor wafers 2 are weighed in a horizontalorientation. The surfaces of the chamber above and below the wafersurface during weighing, i.e. lid 9 and divider 8 are close enough toprevent air convection currents but far enough apart that any residualelectrical charge on the wafer is not attracted to the chamber surfaces.An opening 10 allows access for the robotic arm and wafer.

[0084] The pressure sensor 17, which may be e.g. a Druck PMP4010AB, ismounted so that the sensing port is within the upper balance enclosure.

[0085] The combined temperature & humidity sensor 15, e.g. a Pico RHO2,is also mounted within the upper balance enclosure.

[0086] Any suitable sensors with the appropriate accuracy could be used.

[0087]FIG. 3 shows the arrangement of the thermal transfer plate. Eachwafer 2 is placed in turn onto the upper surface 20 of the plate 5 bythe robotic arm 3. Recesses 11 in the plate allow the robot arm 3 tolower so that the wafer 2 is in contact with the surface 20 of the plate5. A number of grooves 12 in the plate allow trapped air to escape asthe wafer is lowered and prevent it from floating out of position.

[0088] The thermal transfer plate 5 is made from aluminium, although anymaterial with good conductivity could be used. The thermal transferplate equalises the temperature of the wafer to the temperature of thechamber to within +/−0.1° C. This minimises the possibility of anyconvection currents within the balance enclosure and avoids any thermalvariation of the balance that might upset its calibration.

[0089]FIG. 4 shows the control architecture. The balance and robot armcommunicate to a central PC via separate RS232 data links. The combinedTemperature & Humidity sensor, communicates via an additional RS232link. The analogue output of the pressure sensor is converted by a 12bitA/D converter before being transmitted over an IEEE1284 data link.

[0090] To achieve an accurate weighing result, variations in air densitydue to ambient conditions are corrected for. The air density isdetermined and then used to calculate the buoyancy effect on thesemiconductor wafer. The air density is calculated by the followingformula $\rho_{air} = \frac{\begin{matrix}{{0.3485 \times P} - {0.00132 \times}} \\{\left( {{0.0398 \times T^{2}} - {0.1036 \times T} + 9.5366} \right) \times H}\end{matrix}}{\left( {273.14 + T} \right) \times 1000}$

[0091] Where ρ_(air) is the density of the air in g/cm³, P is thepressure in mBar, T is the temperature in ° C. and H is the relativehumidity in %.

[0092] The air density is then used to calculate the buoyancy exerted onthe semiconductor wafer using the following formula:$B = {W_{w} \times \frac{\left( {\frac{\rho_{air}}{\rho_{w}} - \frac{\rho_{air}}{\rho_{c}}} \right)}{1 - \frac{\rho_{air}}{\rho_{w}}}}$

[0093] Where B is the Buoyancy effect in grams, W_(w) is weight of thewafer in grams, ρ_(w) is the density of the wafer in g/cm³ and ρ_(c) isthe density of the calibration weight used to calibrate the weighingbalance in g/cm³.

[0094] The density of the wafer ρ_(w) is well defined due to the purityand crystalline nature of the substrate. The density of single crystalsilicon is 2.329 g/cm³. There is a small error due to the thickness ofthe thin film on the surface.

[0095] A thin film of thickness 0.5 μm and density 1 g/cm3 on a wafer ofthickness 725 μm produces a systematic error of 0.16% in the density.Knowing the approximate target density would allow a correction to bemade, reducing the error still further.

[0096] Finally, the mass of the wafer M_(w) is calculated from theweight W_(w) and the buoyancy B using the formula

M _(w) =W _(w) +B

[0097] Preferably, enhancement would be to use a reference semiconductorwafer as the calibration weight.

[0098] In order to calculate the density of a thin film either depositedor removed from the semiconductor wafer surface two separate weighingmeasurements are made. The wafer is pre-measured, then the wafer issubjected to the process or processes required to deposit or remove thethin film and then it is re-measured afterwards. The difference betweenthe two mass readings provides the mass of the thin film.

[0099] The thickness for insulating dielectrics may be measured usingexisting equipment readily available within semiconductor fabricationfacilities using techniques such as ellipsometry or spectralreflectivity. Typical equipment used for this are the ThermawaveOptiprobe or the Rudolph FEVII.

[0100] Knowledge of the thickness and the mass of the thin film allowsthe density to be determined.

[0101] Alternatively, if the density of the thin film is wellcharacterised then this technique can be used to determine the thicknessof the film without the need for other equipment. In particular, thistechnique is applicable over wide variety of different materialsincluding metals and insulators simultaneously and so is ideal forincorporation into statistical process control environments where ofteneach wafer is measured after each manufacturing process. The weighingequipment can be incorporated into the material handling equipmentwithin semiconductor fabrication facilities. For example, in wafer sort& merge stations, WIP & storage stations or within cluster tool handlingplatforms to provide in-situ process control.

[0102] This technique may also be used to determine the amount ofmaterial removed during etching or CMP processes or for timed etchapplications in damascene trench applications.

[0103] For a particular type of material the density of the thin film islinked to the dielectric constant (relative permittivity) of thematerial by the equation (see also the correlation in FIG. 5)$~{ɛ = \frac{{2 \cdot \alpha \cdot \rho} - ɛ_{0}}{{\alpha \cdot \rho} - ɛ_{0}}}$

[0104] Where ε is the dielectric constant, ε₀ is the permittivity offree space, ρ is the density of the film and ∝ is a constant for thetype of material.

[0105] Using this equation, the density measurement may be used tocalculate the dielectric constant of the thin film.

[0106] As was previously mentioned, the present invention may be used inStatistical Process Control, in which the weight measurement is used asa statistical guide to the accuracy of the processes carried out.

[0107]FIG. 6 depicts a simplified view of part of a typicalsemiconductor fabrication facility. Processing equipment 24 are arrangedin aisles 23 and grouped according to function. Measuring equipment 25are housed in a central location. In an automated facility, cassettes 21of semiconductor wafers are transported using an overhead track system22. Alternatively, Automated Guided Vehicles (AGV) may be used.

[0108] When not being processed, cassettes of wafers are kept insideStockers 26 within a WIP store. A typical processing step involves acentral factory computer determining which process is required next fora particular cassette. The cassette is queued within the Stocker untilthe processing tool is available. The cassette leaves the Stocker, istransported to the processing tool by the overhead track, is processedand then returned to the Stocker.

[0109] Typically, in Statistical process Control environments, thethickness of the layer just deposited or removed from the wafers withinthe cassette will then need to be measured.

[0110] In existing facilities, the central computer must determine theappropriate type of measuring equipment and the wafer is again queuedwaiting for its availability. When available, the cassette leaves theStocker, is transported to the measuring equipment and then returned tothe Stocker to wait for the next processing step.

[0111] An alternative method of operation incorporating the currentinvention is to combine the accurate weighing apparatus of FIG. 1 withthe Stocker 26 within the WIP store. As described previously, theweighing apparatus can be used to determine the amount of materialdeposited or removed from the wafer after each processing step, bycomparison of successive weighing operations. Because the weighingmethod is applicable to a wide range of different materials thiseliminates the need to visit a specific piece of measuring equipmentappropriate to the last processing step. It would not be practical toincorporate all of the existing, different types of measuring equipmentwithin the Stocker 26.

[0112] Incorporating the measurement as part of the Stocker 26 reducesthe number and variety of measuring equipment required in the facility.

[0113] It also reduces the number of material movement operationsrequired, potentially by 50%. This reduces the capacity of the overheadtrack required and improves the cycle time of the facilitysignificantly.

1. A method for determining a dielectric constant of a layer depositedon a semiconductor wafer, the method comprising the steps of determiningthe density of the layer and deriving the dielectric constant of thelayer from the density of the layer using a predefined relationshipbetween the density and the dielectric constant of the layer.
 2. Amethod according to claim 1 wherein the density of the layer isdetermined by: measuring the mass or weight of the layer; measuring thethickness of the layer; and subsequently determining from said thicknessmeasurements and said mass or weight measurements a value representingthe density of the layer.
 3. A method according to claim 2 wherein thestep of measuring the weight or mass of said layer comprises comparingsaid semiconductor wafer both before and after said layer is formedthereon, with a calibration weight having the same density as saidsemiconductor wafer.
 4. A method according to claim 2 wherein the stepof measuring the weight or mass of said layer comprises comparing with areference semiconductor wafer the weight of said semiconductor waferhaving said layer.
 5. A method according to claim 2 wherein the step ofmeasuring the weight or mass of said layer comprises weighing said layerunder vacuum using a balance.
 6. A method according to any of claims 2to 5 wherein a correction is made for the buoyancy exerted on thesemiconductor wafer having said layer by air in the measurement of themass or weight of said layer.
 7. A method according to claim 6, whereinthe buoyancy exerted by air upon the semiconductor wafer is determinedfrom the air density in the chamber which is determined by measuring thetemperature, pressure and humidity in the chamber and calculating theair density from these parameters.
 8. A method according to claim 7wherein the air density is calculated by application of the formula:$\rho_{air} = \frac{\begin{matrix}{{0.3485 \times P} - {0.00132 \times}} \\{\left( {{0.0398 \times T^{2}} - {0.1036 \times T} + 9.5366} \right) \times H}\end{matrix}}{\left( {273.14 + T} \right) \times 1000}$

where ρ_(air) is the density of the air in g/cm³, P is the pressure inmBar, T is the temperature in ° C. and H is the relative humidity in %.9. A method according to claim 7 or claim 8 wherein the air density iscalculated by using two calibration weights of known mass and ofdifferent known density yielding two simultaneous equations involvingthe measured weight and the air density from which the air density iscalculated.
 10. A method according to any of claims 6 to 9 wherein thebuoyancy exerted on the wafer is calculated from the air density, theknown density of the wafer, the density of a calibration weight used tocalibrate the balance and the weight of the wafer by applying thefollowing formula:$B = {W_{w} \times \frac{\left( {{\rho_{air}/\rho_{w}} - {\rho_{air}/\rho_{c}}} \right)}{1 - {\rho_{air}/\rho_{w}}}}$

where B is the Buoyancy effect in grams, W_(w) is weight of the wafer ingrams, ρ_(w) is the density of the wafer in g/cm³ and ρ_(c) is thedensity of the calibration weight used to calibrate the weighing balancein g/cm³.
 11. A method according to any preceding claim wherein thedielectric constant of the material is determined from the densitythereof using the following formula:$~{ɛ = \frac{{2 \cdot \alpha \cdot \rho} - ɛ_{0}}{{\alpha \cdot \rho} - ɛ_{0}}}$

where ε is the dielectric constant, ε₀ is the permittivity of freespace, ρ is the density of the layer and ∝ is a constant for the layer.12. An apparatus for determining the dielectric constant of a layerdeposited on the surface of a semi-conductor wafer, the apparatuscomprising: a weighing chamber containing a weighing instrument to weigha semiconductor wafer, the weighing instrument having means to receive awafer; a temperature sensor, a pressure sensor and a humidity sensor,for monitoring conditions in the weighing chamber; and a processor toreceive measurements from the temperature, pressure and humiditysensors, the processor being arranged to calculate the air-densitywithin the chamber from these measurements, to calculate the buoyancyexerted on the wafer from the calculated air density, to determine themeans of the layer, to determine therefrom the density of the layer, andto determine the dielectric constant of the layer from the density ofthe layer using a predefined relationship between the density and thedielectric constant of the layer.
 13. An apparatus according to claim 12wherein the weighing chamber comprises: a housing having a opening forentry of a wafer; a weighing instrument in the housing to measure theweight of the wafer, the weighing instrument having a balance inconnected to a weighing pan for receiving a wafer; and temperature,pressure and humidity monitors, to determine the temperature, pressureand humidity within the housing.
 14. An apparatus according to any ofclaims 12 or 13 wherein the chamber walls, including the divider, aremade of electrically and/or thermally conductive material.
 15. Anapparatus according to any of claims 12 to 14 wherein the chamberincludes a heater and the interior of the weighing chamber is maintainedat a substantially constant temperature.
 16. An apparatus according toany of claims 12 to 15 further including a thermal transfer plate toreceive a wafer before it is placed on the weighing pan.
 17. Anapparatus according to claim 16 wherein the thermal transfer plate ismade of an electrically and/or thermally conducting material, so thatany static electricity on the wafer is dispersed before measurement. 18.An apparatus according to any of claims 12 to 17 wherein the apparatusfurther includes an anti-static ioniser, comprising a balanced quantityof positive and negative ions used to disperse static electricity withinthe equipment and on the surface of the wafer.
 19. A program for acomputer, the program comprising code to perform the steps of themethods according to any of claims 1 to
 11. 20. A computer programproduct comprising a recording medium on which the computer programaccording to claim 19 is stored.
 21. A method of Statistical ProcessControl for monitoring the statistical variation in properties of layersdeposited on a semiconductor wafer according to one or moremanufacturing processes, and for providing a statistical analysis of theaccuracy of the processes being carried out, wherein measurement of themass of said deposited layers is used to provide said statisticalanalysis.
 22. A method of Statistical Process Control according to claim21 wherein multiple properties of a layer deposited on a semiconductorwafer are determined from a single mass measurement.
 23. A method ofStatistical Process Control according to claim 21 or 22 wherein the massof said deposited layer is measured taking into account the effects ofbuoyancy exerted upon the wafer by the air.
 24. A method of StatisticalProcess Control according to any of claims 21 to 23 wherein the densityof a layer is determined from the measured mass thereof, and thedielectric constant of the layer is determined by applying a predefinedrelationship between the density and the dielectric constant of thelayer to derive from the density the dielectric constant of the layer.25. A method of Statistical Process Control according to claim 24wherein the dielectric constant of the material is determined from thedensity thereof using the following formula:$~{ɛ = \frac{{2 \cdot \alpha \cdot \rho} - ɛ_{0}}{{\alpha \cdot \rho} - ɛ_{0}}}$

where ε is the dielectric constant, ε₀ is the permittivity of freespace, ρ is the density of the layer and ∝ is a constant for the layer.26. A method of Statistical Process Control according to claim 22 or anyof claims 23 to 25 as dependent on claim 22 wherein the multipleproperties of said layer include one or more of: the amount of materialdeposited or removed from a wafer; the thickness of the layer; thedensity of a layer deposited on a wafer; and the dielectric constant ofa layer.